SOLUTION: The sum of four consecutive even integers is1284 the greatest of them is

Question 1101564: The sum of four consecutive even integers is1284 the greatest of them is
Found 2 solutions by Fombitz, greenestamps:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Let the integers be , , , and .
So then the sum is,

Solve for N.
Then find the greatest integer, .

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

It's a bit curious to me that the other tutor chose to call the numbers N-4, N-2, N, and N+2. Most students (and tutors) would probably use N, N+2, N+4, and N+6.

It wouldn't make sense; but you could also represent them with N+30, N+32, N+34, and N+36, or any similar pattern.

And in fact if you are going to choose how to represent the four numbers in a way that makes the arithmetic the easiest, you would represent them with N-3, N-1, N+1, and N+3.

But there is a path to the solution that is faster than any of those choices.

You know the sum of the four numbers is 1284, so the average is 1284/4 = 321.

If the number 321 is the average of 4 consecutive even integers, then the integers are the two even numbers on each side of 321: 318, 320, 322, and 324.
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